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Adapting prediction error estimates for biased complexity selection in high-dimensional bootstrap samples.

Harald Binder1, Martin Schumacher

  • 1Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg. binderh@fdm.uni-freiburg.de

Statistical Applications in Genetics and Molecular Biology
|April 4, 2008
PubMed
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The bootstrap method for evaluating prediction performance can be biased with high-dimensional data. Sampling without replacement offers a promising solution to improve prediction error estimates in such scenarios.

Area of Science:

  • Statistics
  • Bioinformatics
  • Machine Learning

Background:

  • The bootstrap is a resampling technique for evaluating prediction performance without data splitting.
  • High-dimensional data, common in microarrays, presents challenges due to limited observations.
  • Accurate prediction performance evaluation is crucial for reliable statistical modeling.

Purpose of the Study:

  • To investigate the bias in complexity selection within conventional bootstrap samples for high-dimensional data.
  • To evaluate remedies for complexity selection bias, focusing on sampling without replacement.
  • To assess prediction error estimates for high-dimensional binary and time-to-event data.

Main Methods:

  • Simulation studies to assess bias in complexity selection using gradient boosting algorithms.

Related Experiment Videos

  • Comparison of conventional bootstrap (sampling with replacement) against sampling without replacement.
  • Application of a modified bootstrap procedure (.632+) to microarray data for performance evaluation.

    • Main Results:

    • Conventional bootstrap complexity selection is severely biased in many high-dimensional scenarios.
    • Bias in prediction error estimates often leads to underestimation of extractable information.
    • Sampling without replacement effectively mitigates complexity selection bias in various settings.

    Conclusions:

    • Complexity selection bias in bootstrap significantly impacts prediction error estimation for high-dimensional data.
    • Sampling without replacement is a viable and effective strategy to correct this bias.
    • The modified bootstrap procedure demonstrates utility in real-world high-dimensional data analysis, such as in cancer genomics.